Oakland A's officially sign Ryan Madson and John Axford

The Oakland Athletics have officially announced the contracts of relievers Ryan Madson and John Axford after both completed physicals on Thursday:

#Athletics agree to terms with RHP Ryan Madson on a three-year contract and RHP John Axford on a two-year deal pic.twitter.com/gg5LuEqH2a

— Oakland Athletics (@Athletics) December 11, 2015

The A's will pay Madson $22 million over the three years, with the San Francisco Chronicle reporting the breakdown as:

• Signing bonus: $500,000
• 2015: $6.5 million
• 2016: $7.5 million
• 2017: $7.5 million
• Incentives: $250,000 each for finishing 30, 35, and 40 games, and $500,000 for finishing 45 games, each year.

The A's will pay Axford $10 million over the two years, with up to $4 million in games finished bonuses according to Joel Sherman of the New York Post. How he gets there is a little complicated:

axford breakdown: 4.5M '16, 5.5M '17. 1.5M incentives. '17 base in increases by 50 pct of incentives earned. 500K if traded

— Jon Heyman (@JonHeymanCBS) December 12, 2015

So if he earns all $1.5 million in his 2016 incentives, his 2017 base salary would go up $750,000. He would have another chance to earn $1.5 million more in 2017 bonuses, and if he is also traded along the way he earns an assignment bonus of $500,000. That adds up to $4.25 million, so I'll assume Sherman was rounding, I guess.

Oakland's 40-man roster now stands at a full 40 players after the signings, and here's how all 40 players arrived to the A's:

Current payroll for the A's stands at around $77 million as they consider their next moves.